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Non-abelian p-adic L-functions and Eisenstein series of unitary groups - the CM method.

Bouganis, A. (2014) 'Non-abelian p-adic L-functions and Eisenstein series of unitary groups - the CM method.', Annales de l'Institute Fourier., 64 (2). pp. 793-891.

Abstract

In this work we prove various cases of the so-called “torsion congruences” between abelian p-adic L-functions that are related to automorphic representations of definite unitary groups. These congruences play a central role in the non-commutative Iwasawa theory as it became clear in the works of Kakde, Ritter and Weiss on the non-abelian Main Conjecture for the Tate motive. We tackle these congruences for a general definite unitary group of n variables and we obtain more explicit results in the special cases of n = 1 and n = 2. In both of these cases we also explain their implications for some particular “motives”, as for example elliptic curves with complex multiplication. Finally we also discuss a new kind of congruences, which we call “average torsion congruences”.

Item Type:Article
Keywords:p-adic, L-functions, Eisenstein Series, Unitary Groups, Congruences.
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:http://dx.doi.org/10.5802/aif.2866
Date accepted:17 January 2014
Date deposited:28 January 2015
Date of first online publication:02 December 2014
Date first made open access:No date available

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